Design of Built-up Axially Loaded Columns in ChinaBasic Principles of Steel Structures 4.6.1 Design Methods of Built-up Axially Loaded Columns 4.6.2 Design Procedures of Built-up Axially Loaded Columns yyxxColumn limbLacing barFig.14 The common cross-section of the built-up columnFig.15 Laced columnyyxxColumn limbBatten plateFig.16 Battened column4.6.1Design Methods of Built-up Axially Loaded Columns1 1Column limb2 2Lacing systemLacing barBatten plateLacing systemComposition of built-up axially loaded column1.1.4.6.1Design Methods of Built-up Axially Loaded Column Real axis and virtual axis of built-up compression member2.2.（1）Real axisThe centroid axis perpendicular to the plane of the column limby-axis（2）Virtual axisThe centroid axis perpendicular to the plane of lacing bar or batten platex-axisReal axisVirtual axisReal axisVirtual axisFig.17 Real axis and virtual axis4.6.1Design Methods of Built-up Axially Loaded Column Equivalent slenderness ratio3.3.VShear angle 1 1When built-up column buckles about the virtual axis,a large shear deformation may occur in the plane of the lacing bar of batten plate due to the low shear stiffness of the lacing system.2 2The shear deformation will reduce the stability bearing capacity of the member about the virtual axis.3 3We usually use an increased slenderness ratio to consider such a shear effect.The increased slenderness ratio is called the equivalent slenderness ratio,which is represented by 0 x.Fig.18 Shear effect when the column bend about the virtual axisxxyy4.6.1Design Methods of Built-up Axially Loaded Column Equivalent slenderness ratio3.3.Fig.19 Laced column（1）Laced columnxslenderness ratio of the built-up column about the virtual axis;yyxxColumn limbLacing barAthe overall gross cross-sectional area of the built-up column;A1the sum of the gross cross-sectional area of the diagonal lacing bars.(4-13)4.6.1Design Methods of Built-up Axially Loaded Column Equivalent slenderness ratio3.3.（2）Battened columnxslenderness ratio of the built-up column about the virtual axis;1 slenderness ratio of a single column limb about its centroid axis 1-1.yyxxColumn limbBatten plateFig.20 Battened column11(4-14)4.6.1Design Methods of Built-up Axially Loaded Column Calculated length and slenderness ratio of a single column limb4.4.yyxxColumn limbBatten plateFig.22 Battened columnl1Fig.21 Laced columnyyxxColumn limbLacing barl1114.6.1Design Methods of Built-up Axially Loaded Column Global buckling design formula about the virtual axis5.5.（1）Global buckling about real axisCalculation formula of the overall stability of built-up column about the real axis is the same as that of the solid-web columns.（2）Global buckling about virtual axisEquivalent slenderness ratio 0 x must be used to derive the corresponding stability coefficient x.(4-15)(4-16)4.6.1Design Methods of Built-up Axially Loaded Column Global buckling of single column limb6.6.（1）Laced Column（2）Battened Column(4-17)(4-18)4.6.2Design Procedures of Built-up Axially Loaded ColumnsDesign Procedures1.1.1 1Assume a slenderness ratio about the real axis y=50-100.Determine the value of the overall stability coefficient y and the required cross-sectional area.2 2Select an appropriate type of section steel as the trial section of the column limb based on the obtained cross-sectional area A.yy(4-19)3 3Determine the distance between the two-column limbs according to the principle of equivalent stabilityDesign Procedures1.1.According to（Laced column）（Battened column）Determine the width of the column4.6.2Design Procedures of Built-up Axially Loaded Columns4 4Verify the overall stability of the column about the virtual axis.If the stability is not satisfied,adjust the distance between the two-column limbs to ensure the stability bearing capacity.5 5Verify the overall stability of the column limb.Design Procedures1.1.6 6Design the lacing bar and batten plate.4.6.2Design Procedures of Built-up Axially Loaded Columns